Numerical Integration of MeijerG function in the form MeijerG[{{-2,-8.5,-3.5},{}},{{0},{-1.5}},theta]

The trick seems to be to FunctionExpand the MeijerG function before integration:

a[θ_] = MeijerG[{{-2, -17/2, -7/2}, {}}, {{0}, {-3/2}}, θ] // FunctionExpand // FullSimplify
(*    (Sqrt[π] Sqrt[θ] (128 + θ (4416 + θ (50048 + θ (213120 - 7 θ (-36608 + 3 θ (3168 + 5 θ (-432 + θ (400 + 9 θ (-40 + θ (18 + 11 θ)))))))))) -
      32 E^(1/θ) π (4 + 7 θ (20 + θ (233 + 34 θ (31 + 45 θ)))) Erfc[1/Sqrt[θ]])/(128 θ^(27/2))    *)

Integrate[a[θ], {θ, 0, π/2}]
(*    (1/(1024 π^(21/2)))(-2097152 - 24117248 π - 78643200 π^2 - 65601536 π^3 + 9732096 π^4 - 3870720 π^5 + 2150400 π^6 - 1209600 π^7 + 362880 π^8 + 166320 π^9 + 30405375 π^11 + 262144 Sqrt[2] E^(2/π) (8 + π (94 + 7 π (46 + 45 π))) Erfc[Sqrt[2/π]])    *)

% // N
(*    52664.9    *)